Furring strips required over 1" rigid foam insulation?

Planning the renovation of a 110 year-old cottage in Indianapolis. Looking to put 1" of rigid foam on the outside before re-siding with fiber cement lapboards, and 3.5" of wet spray cellulose inside. We do have wood sheathing, horizontally hung 1x boards, on the exterior of the wall studs.

Is the furring strip over the foam advisable because it will 1) allow air circulation behind the siding or 2) provide structural support when hanging siding? Or both?

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William,
The James Hardie Co. allows its fiber-cement lap siding to be installed over 1 inch of rigid foam without any intervening furring strips. According to Hardie, "Hardiplank lap siding can also be installed over foam insulation up to 1” thick. ... For application over foam insulation, the length of the specified fastener shall be increased by the thickness of the foam insulation."

In my opinion, however, installation over a ventilated rainscreen gap (created by vertical furring strips installed over the rigid foam) is better. With an air gap behind the siding, the siding dries faster, and the siding is less stressed by differences in the moisture content between the face of the siding and the back of the siding. The rainscreen gap may also help the paint last longer.

With furring through-screwed 24" on center, you have far fewer fasteners penetrating and thermally bridging the foam, making for better air tightness and getting the full R out of the foam. With 10,001 long-nails pounded through to hold up the fiber cement there's no chance of the foam being air tight on day-1 let alone over time. And every nail will conduct as much heat as a few square inches of foam, reducing it's insulating function.